BODRUM, Turkey — As darkness falls and the last of the shorefront cafes in Bodrum clear their tables for the night, dozens of migrants pour out of a waiting bus. In the gloam, they charge for the sea, dragging a large rubber dinghy.

Their smugglers point them toward the flashing lighthouse on the Greek island of Kos, as little as 25 minutes away in a good boat.

In their flimsy inflatables, they usually reach there by dawn, quickly puncture their dinghies so no one can force them back, then walk into town.

Viewed from either side, the passage, while risky, is remarkably organized and unfettered. Compared with other routes for migrants crossing the Mediterranean, where more than 2,000 people have died this year, it is a relatively first-class ride. So easy and efficient is it, in fact, that in July the route was used by more than 7,000 refugees — most fleeing wars in Afghanistan, Iraq and Syria. At least 2,000 crossed this past week alone.

The human tide has overwhelmed the island of Kos, leading its mayor, George Kiritsis, to predict that if he does not get help from Athens, “blood will be shed.” And it has left Greece — for now, foremost in Europe — struggling to balance how to humanely accommodate the refugees against the risk of encouraging still more.

Already, for those who have made the journey, seeking safety, opportunity and a new life, the welcome has been less than hoped for.

“In Istanbul, they let us use the toilets for free,” said Ayman Almotlak, 31, a Syrian who teaches Arabic and made the crossing to Kos, speaking of the local merchants. “Here not. Why do the Greeks hate us?”

Part of the reason is the sheer magnitude of the wave of migrants and refugees, which the Greek government has said is too much for such a crisis-ridden country — let alone an island like Kos — to handle.

Doctors Without Borders complained that the Greek authorities were “abusing” the refugees by, at one point last week, forcing them into a stadium where they remained without proper hygiene, food or water.

The International Organization for Migration, based in Geneva, said Friday that nearly 250,000 migrants had crossed the Mediterranean to Europe this year, already more than for all of 2014. Greece alone, it said, had reported 134,988 arrivals from Turkey this year.

For many of the refugees, Greece is seen as a steppingstone to Western Europe. Although Turkey is hosting nearly two million Syrian refugees, more than any other country, many Syrians say that they do not see a future there.

To get to Europe, they depend on a vast illegal migrant smuggling operation that has grown over the past year as the Syrian civil war grinds on.

“A year ago people were still hopeful that the war might end, but now, with no end in sight, people want to leave and build a new life,” said Bashar, 32, a Syrian refugee in Bodrum, who did not want to give his last name. He had spent the past year in Turkey getting surgery after he was wounded by a barrel bomb.

In Bodrum, smugglers charge between $1,000 to $1,500 per person to transfer the migrants to Kos. The price includes the rubber boat and training some of the passengers on how to steer it.

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Migrants crowd a boat leaving Bodrum, Turkey, for a Greek island, a trip that takes just hours and costs up to $1,500.CreditBulent Kilic/Agence France-Presse — Getty Images

Life jackets are not included and are discouraged by some smugglers, who argue that they take up too much space.

On a recent night in Bodrum after two of the boats took off, life jackets, socks and backpacks were scattered across the beach.

“The smugglers are cruel — they don’t treat the refugees like humans,” said Senol Bayrak, a local fisherman who observes the activity in the area. “For them every meter of that boat is a dollar and it counts.”

Turkish authorities have been accused of turning a blind eye to the crisis unfolding along the country’s southern shores, and allowing the refugees to pass through, something that has generated increasing tensions with their Greek counterparts.

Residents say that hundreds of boats leave throughout the night, and are intercepted only once citizens alert the authorities.

On Thursday night, residents watched as one of the boats left the shore and drifted in the direction opposite to Kos. Once the boat was out of sight, distressed shouts could be heard in the distance, prompting the residents to call the Coast Guard, who later intercepted the boat.

“They come when we call them, but they need to do more,” said Erol, 69, a retired captain, who would give only his first name.

But the local military police insist that they are doing everything in their power to prevent the refugees from leaving via illegal and dangerous routes.

They say that they carry out extensive daily patrols, but that the vast numbers of migrants trying to leave at once is “unmanageable.”

“We are in close coordination with the coast guards, who are working hand in hand with Greece to save lives,” a senior Turkish military police chief said on the condition of anonymity because he was not authorized to speak on the matter.

“The greatest obstacle is proving that they are planning to leave and catching out the smugglers who hide within their opaque network,” he said as he looked out at the garden of the police station, where detained migrants lay listlessly under the trees.

A total of 1,799 illegal migrants trying to get to Greece were picked up on the Aegean in 44 separate operations from Aug. 7 to Aug. 10, while two human traffickers were also detained, the Turkish Coast Guard Command said.

Among the refugees, the Syrians, who tend to be more middle class, come the most well-equipped. They almost always have cellphones and GPS, and they have memorized every step they must take as they head out of Greece and toward their destination, greater Europe.

“I have a map,” said Mr. Almotlak, the Syrian teacher, tapping his head. “It is here — and on Google Maps.”

Once in Greece, the smugglers organize trips for the migrants, give them tips and connect them with buses, trains and taxis, all for a prearranged fee, while merchants sell them gear, such as tents.

Pack your 500-euro notes in zip-lock bags and carry them in your underwear, they are told. Download WhatsApp, so you can send instant messages.

The profiteering is both large and small. The passage from Bodrum to Kos might cost about $1,500, but once in Kos, Greek merchants also make money by selling equipment or charging as much as 4 euros, about $4.40, the price of a cappuccino, just to use the bathroom.

While many Greeks have extended their hospitality, providing food and water to the migrants, others resent their presence in the midst of the tourist season.

The tension has eased over the past few days, as the Greek government heeded the mayor’s request to send reinforcements and relief to Kos, where refugees are camped out.

Athens has sped up the evacuation of the refugees by sending a dozen more people to process their papers, adding to the four or five who had been doing it. That has allowed more than 1,000 people a day to leave the island on ferryboats for Piraeus, the port of Athens.

Yet the Syrians are a privileged class among the migrants. At home, Syrians have suffered during the lengthy civil war. But on Kos, being a Syrian is a badge of honor and, many of the refugees from elsewhere believe, a ticket to Europe.

Authorities say that among the migrants, there are hundreds — from places like Iraq, Iran or Afghanistan — who are posing as Syrians.

In Kos, Syrians have been given priority for lodgings in a huge ferryboat that docked at the island on Friday, intended to be used as a dormitory ship for migrants camped on the promenade and in public plazas.

At the opposite extreme from the Syrians are about 500 migrants from countries like Pakistan and Bangladesh who have been squatting in an abandoned hotel outside town, squeezed into about 60 rooms, with running water but no electricity.

Because the Syrians are from a war-torn country, the Greeks give them papers allowing them to stay in the country for longer than others.

Most do not want to stay in Greece, but this gives them time to make the trip north.

When they cross the border, they are in limbo again, and can be sent back, they say. So they avoid places like Western Union, where the police may lurk.

Instead, many carry cash or pick it up from middlemen along the way. Their goal is to make it to a country like Germany or Sweden and request asylum, then bring their families.

Mr. Almotlak calculated two possible routes: to Britain or to Germany. He settled on Germany, even though he preferred England, because of the cost.

He could travel from Syria to Germany for €3,000 to €4,000, he said, but England could take €10,000 or €12,000.

On Saturday morning, Mosaab Alhamed, 32, a Syrian who has a law degree and owned a grocery store with his father and brother, and 41 others, including nine women and two children, made their second attempt to reach Kos.

Their overloaded boat puttered along for three hours, the Kos harbor lights shimmering like a mirage in the distance. Within a kilometer of Kos, a Greek police boat approached the boat and an officer cried out “Stop! Stop!” in English, Mr. Alhamed said a few hours later. When the refugees kept going, the officer fired a warning shot into the air, making Mr. Alhamed’s heart pound. This time the boat stopped and the police towed it to shore, then let the passengers go.

That night, Mr. Alhamed and two friends shared a €50 hotel room, showered and rested. At a souvlaki restaurant, they debated whether to go to Athens next or straight to Thessaloniki, before continuing, probably to Germany.

He had not been traumatized by his trip, Mr. Alhamed said, his blue eyes crinkling in a warm smile. The war in Syria was much worse. His family grocery had been bombed and destroyed, his home occupied by the regime and his three dogs killed. He wondered what had happened to his cat.

As he spoke, Mr. Alhamed tossed scrap after scrap of his uneaten chicken schnitzel to cats in the restaurant. “I love cats,” he said, wistfully.

Correction:

An earlier version of a picture caption in the slide show with this article misidentified the home country of one refugee, Laith Majid. He is from Iraq, not Syria. Because of an editing error, an earlier version of the reporting credit with this article misspelled the surname of one of the reporters. She is Ceylan Yeginsu, not Teginsu.